Free Grade 3 Introduction to Introducing Sine Rule Essentials Flashcards
Free Grade 3 flashcards for Introduction to Introducing Sine Rule Essentials: 12 real questions with a full answer key and worked solutions. In a right-angled triangle, a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle). Trigonometry links the sides to the angles.
Free
Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introduction to introducing sine rule essentials
Identify introduction to introducing sine rule essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introduction to introducing sine rule essentials
Explain introduction to introducing sine rule essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to introducing sine rule essentials
Calculate introduction to introducing sine rule essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to introducing sine rule essentials
Compare introduction to introducing sine rule essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Introduction to Introducing Sine Rule Essentials works
In a right-angled triangle, a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle). Trigonometry links the sides to the angles.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.A right-angled triangle has shorter sides 8 cm and 15 cm. Find the hypotenuse.[1]
- 2.A right-angled triangle has shorter sides 7 cm and 24 cm. Find the hypotenuse.[1]
- 3.A right-angled triangle has shorter sides 3 cm and 4 cm. Find the hypotenuse.[1]
- 4.A right-angled triangle has shorter sides 5 cm and 12 cm. Find the hypotenuse.[1]
- 5.A right-angled triangle has hypotenuse 15 cm and one side 9 cm. Find the other side.[2]
- 6.A right-angled triangle has hypotenuse 13 cm and one side 5 cm. Find the other side.[2]
- 7.A right-angled triangle has hypotenuse 25 cm and one side 7 cm. Find the other side.[2]
- 8.A right-angled triangle has hypotenuse 5 cm and one side 3 cm. Find the other side.[2]
- 9.In a right-angled triangle, the side opposite angle θ is 8 cm and the hypotenuse is 17 cm. Find θ to 1 d.p.[3]
- 10.In a right-angled triangle, the side opposite angle θ is 6 cm and the hypotenuse is 10 cm. Find θ to 1 d.p.[3]
- 11.In a right-angled triangle, the side opposite angle θ is 3 cm and the hypotenuse is 5 cm. Find θ to 1 d.p.[3]
- 12.In a right-angled triangle, the side opposite angle θ is 9 cm and the hypotenuse is 15 cm. Find θ to 1 d.p.[3]
Show answers and working
1. 17 cm
c² = a² + b² = 64 + 225 = 289. c = √289 = 17 cm.
2. 25 cm
c² = a² + b² = 49 + 576 = 625. c = √625 = 25 cm.
3. 5 cm
c² = a² + b² = 9 + 16 = 25. c = √25 = 5 cm.
4. 13 cm
c² = a² + b² = 25 + 144 = 169. c = √169 = 13 cm.
5. 12 cm
b² = c² − a² = 225 − 81 = 144. b = √144 = 12 cm.
6. 12 cm
b² = c² − a² = 169 − 25 = 144. b = √144 = 12 cm.
7. 24 cm
b² = c² − a² = 625 − 49 = 576. b = √576 = 24 cm.
8. 4 cm
b² = c² − a² = 25 − 9 = 16. b = √16 = 4 cm.
9. 28.1°
sin θ = opposite / hypotenuse = 8/17. θ = sin⁻¹(0.4706) = 28.1°.
10. 36.9°
sin θ = opposite / hypotenuse = 6/10. θ = sin⁻¹(0.6) = 36.9°.
11. 36.9°
sin θ = opposite / hypotenuse = 3/5. θ = sin⁻¹(0.6) = 36.9°.
12. 36.9°
sin θ = opposite / hypotenuse = 9/15. θ = sin⁻¹(0.6) = 36.9°.
Worked examples
A right-angled triangle has shorter sides 9 cm and 12 cm. Find the hypotenuse.
- c² = a² + b² = 81 + 144 = 225.
- c = √225 = 15 cm.
- Answer: 15 cm
A right-angled triangle has hypotenuse 10 cm and one side 6 cm. Find the other side.
- b² = c² − a² = 100 − 36 = 64.
- b = √64 = 8 cm.
- Answer: 8 cm
In a right-angled triangle, the side opposite angle θ is 5 cm and the hypotenuse is 13 cm. Find θ to 1 d.p.
- sin θ = opposite / hypotenuse = 5/13.
- θ = sin⁻¹(0.3846) = 22.6°.
- Answer: 22.6°
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Adds the squares when finding a shorter side.
Correction: Shorter side: subtract from the hypotenuse squared.
Forgets to square root at the end.
Correction: c² is not c — finish with √.
Teacher tips
- · Label the hypotenuse first every time.
Parent tips
- · Measure a phone screen's sides and check the diagonal.
Real-life applications
- · Ladder length against a wall, TV screen sizes.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Introduction to Introducing Sine Rule Essentials
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Introduction to Introducing Sine Rule Essentials flashcards really free?
- Yes. Every flashcards on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Right-angled Trigonometry. Each one has its own free lesson, worksheet and quiz.
- How is the flashcards sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Introduction to Introducing Sine Rule Essentials?
- Move on to Key Vocabulary of Introducing Sine Rule Essentials, Rules and Methods in Introducing Sine Rule Essentials, Working with Introducing Sine Rule Essentials, Introducing Sine Rule Essentials in Examinations, which build directly on this idea.
Related resources
- Free Introduction to Introducing Sine Rule Essentials worksheets
- Free Introduction to Introducing Sine Rule Essentials quizzes
- Free Introduction to Introducing Sine Rule Essentials lessons
- Free Introduction to Introducing Sine Rule Essentials lesson plans
- Introduction to Introducing Sine Rule Essentials in the knowledge graph
- Free AI Tutor
Stuck on Introduction to Introducing Sine Rule Essentials? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor